On a brief but thrilling final morning in Hobart, Western Australia got the margin down to within seven runs of their target of 259 with two wickets in hand.
But after appearing as if he would be the hero for the visitors, left-hander Joel Curtis was adjudged lbw on 50 by a Riley Meredith ball that stayed low from around the wicket.
Jackson Bird then trapped No.11 Liam Haskett lbw with an in-swinging yorker, ending Western Australia's chase to have them all out for 255.
Tasmania's win is the equal-fifth closest in the Shield's 134-season history in terms of runs, and comes after Western Australia held just a one-run advantage in the first innings.
It also follows Tasmania's narrow loss to South Australia last summer, when they were beaten by two runs in Hobart.
For much of Saturday morning it appeared as if Western Australia would pull off an unlikely victory.
Needing 44 to win at the start of the day, Curtis and Corey Rocchicchioli (23no) appeared to have the game under control with a 52-run ninth-wicket stand.
Curtis had done his best to shield Rocchicchioli from the strike for parts of Saturday morning, but when the No.10 was exposed he still managed to thrive.
He clipped one Bird ball to the mid-wicket boundary off his pads and cut the first delivery of Meredith's spell for four when Tasmania brought the quick on.
Curtis did have one near-miss before his dismissal with a bottom-edge to a cut shot from Gabe Bell narrowly evading off stump and running away to the boundary.
But just as the pair got the margin required to single figures and began to look confident of victory, it was Meredith and Bird who turned the game on its head.
The result leaves Western Australia with two losses after the opening two rounds, while Tasmania's win comes after they drew with Queensland in their season opener.
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